Nuprl Lemma : mon_ident_q
∀[a:ℚ]. (((a + 0) = a ∈ ℚ) ∧ ((0 + a) = a ∈ ℚ))
Proof
Definitions occuring in Statement :
qadd: r + s,
rationals: ℚ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
abgrp: AbGrp,
grp: Group{i},
mon: Mon,
imon: IMonoid,
prop: ℙ,
qadd_grp: <ℚ+>,
grp_car: |g|,
pi1: fst(t),
grp_op: *,
pi2: snd(t),
grp_id: e,
infix_ap: x f y
Lemmas referenced :
mon_ident,
qadd_grp_wf,
grp_sig_wf,
monoid_p_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
inverse_wf,
grp_inv_wf,
comm_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
applyEquality,
sqequalRule,
lambdaEquality_alt,
setElimination,
rename,
hypothesisEquality,
setIsType,
universeIsType,
because_Cache
Latex:
\mforall{}[a:\mBbbQ{}]. (((a + 0) = a) \mwedge{} ((0 + a) = a))
Date html generated:
2020_05_20-AM-09_13_45
Last ObjectModification:
2020_01_28-PM-03_40_52
Theory : rationals
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