Nuprl Lemma : int_term_ind-sub
∀[C,V,A,S,M,MN,a,b:Top].
(int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
(a (-) b) ~ S[a;b;int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
a;int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
b])
Proof
Definitions occuring in Statement :
int-term-ind-fun: int-term-ind-fun,
itermSubtract: left (-) right,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
so_apply: x[s],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
int-term-ind-fun: int-term-ind-fun,
itermSubtract: left (-) right,
int_term_ind: int_term_ind,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[C,V,A,S,M,MN,a,b:Top].
(int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
(a (-) b) \msim{} S[a;b;int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
a;int-term-ind-fun(c.C[c];
v.V[v];
l,r,rl,rr.A[l;r;rl;rr];
l,r,rl,rr.S[l;r;rl;rr];
l,r,rl,rr.M[l;r;rl;rr];
x,rx.MN[x;rx])
b])
Date html generated:
2017_09_29-PM-05_52_02
Last ObjectModification:
2017_05_12-PM-00_13_51
Theory : omega
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