Nuprl Lemma : exp-fastexp
∀[i:ℤ]. ∀[n:ℕ]. (i^n ~ i^n)
Proof
Definitions occuring in Statement :
fastexp: i^n,
exp: i^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fastexp: i^n,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_exists: ∃x:A [B[x]],
prop: ℙ,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T}
Lemmas referenced :
efficient-exp-ext,
subtype_rel_self,
all_wf,
nat_wf,
sq_exists_wf,
equal-wf-base,
istype-nat,
istype-int,
subtype_base_sq,
int_subtype_base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
functionEquality,
closedConclusion,
intEquality,
Error :lambdaEquality_alt,
because_Cache,
Error :inhabitedIsType,
hypothesisEquality,
Error :lambdaFormation_alt,
Error :equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomSqEquality,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
setElimination,
rename,
cumulativity,
independent_isectElimination
Latex:
\mforall{}[i:\mBbbZ{}]. \mforall{}[n:\mBbbN{}]. (i\^{}n \msim{} i\^{}n)
Date html generated:
2019_06_20-PM-02_31_50
Last ObjectModification:
2018_11_28-PM-07_12_43
Theory : num_thy_1
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