Nuprl Lemma : int-term-ind-fun_wf
∀[A:Type]. ∀[v:int_term()]. ∀[Constant,Var:var:ℤ ⟶ A]. ∀[Add,Subtract,Multiply:left:int_term()
⟶ right:int_term()
⟶ A
⟶ A
⟶ A].
∀[Minus:num:int_term() ⟶ A ⟶ A].
(int-term-ind-fun(c.Constant[c];
v.Var[v];
l,r,rl,rr.Add[l;r;rl;rr];
l,r,rl,rr.Subtract[l;r;rl;rr];
l,r,rl,rr.Multiply[l;r;rl;rr];
x,rx.Minus[x;rx]) ∈ int_term() ⟶ A)
Proof
Definitions occuring in Statement :
int-term-ind-fun: int-term-ind-fun,
int_term: int_term(),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-term-ind-fun: int-term-ind-fun,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
int_term_ind_wf_simple,
int_term_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
applyEquality,
functionExtensionality,
intEquality,
because_Cache,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[v:int\_term()]. \mforall{}[Constant,Var:var:\mBbbZ{} {}\mrightarrow{} A]. \mforall{}[Add,Subtract,Multiply:left:int\_term()
{}\mrightarrow{} right:int\_term()
{}\mrightarrow{} A
{}\mrightarrow{} A
{}\mrightarrow{} A].
\mforall{}[Minus:num:int\_term() {}\mrightarrow{} A {}\mrightarrow{} A].
(int-term-ind-fun(c.Constant[c];
v.Var[v];
l,r,rl,rr.Add[l;r;rl;rr];
l,r,rl,rr.Subtract[l;r;rl;rr];
l,r,rl,rr.Multiply[l;r;rl;rr];
x,rx.Minus[x;rx]) \mmember{} int\_term() {}\mrightarrow{} A)
Date html generated:
2017_09_29-PM-05_51_55
Last ObjectModification:
2017_05_12-AM-11_49_48
Theory : omega
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