Nuprl Lemma : fun_exp_add-sq
∀[n,m:ℕ]. ∀[f,x:Top]. (f^n + m x ~ f^n (f^m x))
Proof
Definitions occuring in Statement :
fun_exp: f^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
add: n + m,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
top_wf,
nat_wf,
fun_exp0_lemma,
zero-add,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
fun_exp_add_sq,
le_weakening2,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
sqequalAxiom,
voidEquality,
because_Cache,
unionElimination,
independent_pairFormation,
productElimination,
addEquality,
applyEquality,
intEquality,
minusEquality,
dependent_set_memberEquality
Latex:
\mforall{}[n,m:\mBbbN{}]. \mforall{}[f,x:Top]. (f\^{}n + m x \msim{} f\^{}n (f\^{}m x))
Date html generated:
2016_05_13-PM-04_07_04
Last ObjectModification:
2015_12_26-AM-11_04_17
Theory : fun_1
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