Nuprl Lemma : conj_perm_wf
∀n:ℕ. ∀p,q:Sym(n). (conj{p}(q) ∈ Sym(n))
Proof
Definitions occuring in Statement :
conj_perm: conj{p}(q),
sym_grp: Sym(n),
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
conj_perm: conj{p}(q),
uall: ∀[x:A]. B[x],
nat: ℕ,
sym_grp: Sym(n)
Lemmas referenced :
comp_perm_wf,
int_seg_wf,
inv_perm_wf,
perm_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
inhabitedIsType,
universeIsType
Latex:
\mforall{}n:\mBbbN{}. \mforall{}p,q:Sym(n). (conj\{p\}(q) \mmember{} Sym(n))
Date html generated:
2019_10_16-PM-00_59_46
Last ObjectModification:
2018_10_08-AM-09_20_26
Theory : perms_1
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