Nuprl Lemma : fan-iff-wkl!
Fan ⇐⇒ WKL!
Proof
Definitions occuring in Statement :
wkl!: WKL!,
fan: Fan,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A
Lemmas referenced :
dfan-iff-twkl!,
bool_wf,
fan-iff-dfan-bool,
wkl!-iff-twkl!-bool,
fan_wf,
wkl!_wf,
iff_wf,
dfan_wf,
twkl!_wf,
false_wf,
le_wf,
equipollent-two,
equipollent_wf,
int_seg_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesis,
independent_functionElimination,
addLevel,
productElimination,
independent_pairFormation,
impliesFunctionality,
instantiate,
isectElimination,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
lambdaFormation,
hypothesisEquality,
setElimination,
rename
Latex:
Fan \mLeftarrow{}{}\mRightarrow{} WKL!
Date html generated:
2016_05_14-PM-04_12_50
Last ObjectModification:
2015_12_26-PM-07_53_58
Theory : fan-theorem
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