Nuprl Lemma : fun_exp_add1-sq
∀[n:ℕ]. ∀[f,x:Top]. (f (f^n x) ~ f^n + 1 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,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
top: Top,
compose: f o g
Lemmas referenced :
fun_exp_add-sq,
false_wf,
le_wf,
top_wf,
nat_wf,
fun_exp1_lemma,
add-commutes
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
isect_memberFormation,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,x:Top]. (f (f\^{}n x) \msim{} f\^{}n + 1 x)
Date html generated:
2016_05_13-PM-04_07_06
Last ObjectModification:
2015_12_26-AM-11_04_14
Theory : fun_1
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